Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Lagrange-Galerkin methods on spherical geodesic grids
Journal of Computational Physics
Spatial discretization of the Shallow water equations in spherical geometry using Osher's scheme
Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Short Note: An explicit expression for the penalty parameter of the interior penalty method
Journal of Computational Physics
Journal of Computational Physics
Unsteady analytical solutions of the spherical shallow water equations
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
LBB stability of a mixed Galerkin finite element pair for fluid flow simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
Numerical wave propagation for the triangular P1DG-P2 finite element pair
Journal of Computational Physics
Hi-index | 31.45 |
We study the applicability of a new finite element in atmosphere and ocean modeling. The finite element under investigation combines a second order continuous representation for the scalar field with a first order discontinuous representation for the velocity field and is therefore different from continuous and discontinuous Galerkin finite element approaches. The specific choice of low order approximation spaces is attractive because it satisfies the Ladyzhenskaya-Babuska-Brezzi condition and is, at the same time, able to represent the crucially important geostrophic balance. The finite element is used to solve the viscous and inviscid shallow water equations on a rotating sphere. We introduce the spherical geometry via a stereographic projection. The projection leads to a manageable number of additional terms, the associated scaling factors can be exactly represented by second order polynomials. We perform numerical experiments considering steady and unsteady zonal flow, flow over topography, and an unstable zonal jet stream. For ocean applications, the wind driven Stommel gyre is simulated. The experiments are performed on icosahedral geodesic grids and analyzed with respect to convergence rates, conservation properties, and energy and enstrophy spectra. The results match quite well with results published in the literature and encourage further investigation of this type of element for three-dimensional atmosphere/ocean modeling.